We report on the behavior of a high-T c superconducting (HTS) homopolar dynamo which outputs a DC open-circuit voltage when the stator is in the superconducting state, but behaves as a conventional AC alternator when the stator is in the normal state. We observe that this time-averaged DC voltage arises from a change in the shape of the AC voltage waveform that is obtained from a normal conducting stator. The measured DC voltage is proportional to frequency, and decreases with increasing flux gap between the rotor magnet and the HTS stator wire. We observe that the DC output voltage decreases to zero at large flux gaps, although small differences between the normal-conducting and superconducting waveforms are still observed, which we attribute to screening currents in the HTS stator wire. Importantly, the normalised pulse shape is found to be a function of the rotor position angle only. Based on these observations, we suggest that the origin of this unexpected DC effect can be explained by a model first proposed by Giaever, which considers the impact of time-varying circulating eddy currents within the HTS stator wire. Such circulating currents form a superconducting shunt path which "short-circuits" the high field region directly beneath the rotor magnet, at those points in the cycle when the rotor magnet partially overlaps the superconducting stator wire. This reduces the output voltage from the device during these periods of the rotor cycle, leading to partial rectification of the output voltage waveform and hence the emergence of a time-averaged DC voltage.